Mathematics High School

2.4 + 5.4q – 4.5q + 3.6

a.6+1.1q
b.9.9q+6
c.0.9q+6
d.9.9q-6

Answers

Answer 1
You have to add the same kind of terms, in this case the ones that have a variable (5.4q and -4.5q) and the ones that don't (2.4 and 3.6), like this:

(5.4q - 4.5q) + (2.4 + 3.6) = 0.9q + 6

The answer is c. 0.9 +6

Answer 2

Answer:

c!

Step-by-step explanation:

i did the test loll <3

Related Questions

Part 1.] Indicate the general rule for the arithmetic sequence with [tex] a_{3}=-4[/tex] and [tex] a_{8}=-29[/tex]
A.] [tex] a_{n}=-6+(n-1)(-5)[/tex]
B.] [tex] a_{n}=-6+(n-1)(5)[/tex]
C.] [tex] a_{n}=6+(n-1)(-5)[/tex]
D.] [tex] a_{n}=6+(n-1)(5)[/tex]

Part 2.] Which of the following is the general term for the sequence m, -m, m, -m, . . .?
A.] [tex]m(-1)^{n-1}[/tex]
B.] [tex](-m)^{n}[/tex]
C.] [tex](-1)m^{n+1}[/tex]
D.] [tex](-1)m^{n-1}[/tex]

Part 3.] Indicate a general rule for the [tex] n^{th}[/tex] term of the sequence when [tex] a_{1}=5[/tex] and [tex]r= \sqrt{3}[/tex]
A.] [tex] a_{n}=( \sqrt{3})(5)^{n+1}[/tex]
B.] [tex] a_{n}=( \sqrt{3})(5)^{n-1}[/tex]
C.] [tex] a_{n}=(5)( \sqrt{3})^{n-1}[/tex]
D.] [tex] a_{n}=(5)( \sqrt{3})^{n+1}[/tex]

Answers

These are 3 questions and 3 answers.

Part 1.] Indicate the general rule for the arithmetic sequence with A3 = - 4 and A8 = - 29

Answer: option C. An = 6 + (n-1)(-5)

Solution:

1) A3 is the third term
2) A8 is the eigth term
3) The formula for arithmetic sequences is: An = Ao + (n - 1)d

where n is the number of term and d is the difference between two consecutive terms.

=>

4) A8 = Ao + (8 - 1)d = - 29 => Ao + 7d = - 29  ----- [equation 1]

5) A3 = Ao + (3 - 1)d = - 4 => Ao + 2d = - 4 ------- [equation 2]

6) Subtract equation 2 from equation 1 => 7d - 2d = - 29 - (-4) =>

5d = - 29 + 4
5d = - 25
d = - 25/5 = - 5

7) Find Ao using equation 2:

 Ao + 2d = - 4 =>
 Ao = - 4 - 2d = - 4 - 2(- 5) = - 4 + 10 = 6

8) General rule: An = 6 + (n - 1) (-5) <-------- answer: option C.
 

Part 2.] Which of the following is the general term for the sequence m, -m, m, -m, . . .?

Answer: option a. m (-1)^ (n-1).

Justification:

the sign of the coefficient changes for each term.

when n = 1, the sign is positive: (-1)^ (1-1) = 1
when n = 2, the sign is  negative: (-1)^ (2-1) = - 1
when n = 3, the sign is positive: (-1)^ (3-1) = 2

And so on. So, m (-1)^ (n-1) does the work.

Part 3.] Indicate a general rule for the nth term of the sequence when A1 = 5 and r = √3


Answer: option C. An = (5)(√3)^(n-1)

Explanation:

This is a geometric sequence with A1 = 5 and r = √3

The terms of the geometric sequence are:

A1 = 5
A2 = A1 * √3 = 5√3
A3 = A2 * √3 = 5(√3)(√3) = 5(3) = 15
A4 = A3 * √3 = 15√3

So, the general expression is An = 5 * (√3)^(n-1), which is the option C.

A new softball dropped onto a hard surface from a height of 25 inches rebounds to about 2/5 the height on each successive bounce. (a) Write a function representing the rebound height for each bounce. (b) Graph the function. (c) After how many bounces would a new softball rebound less than 1 inch?

f(x) = 25(0.4)x; 6 bounces.
f(x) = 0.4(25)x; 6 bounces.
f(x) = 25(0.4)x; 4 bounces.
f(x) = 0.4(25)x; 4 bounces.

Answers

let f(x) be the height reached after x=0,1,2,3....
f(0) be the original height f(0)=25 in
then:
f(x)=f(0)(0.40)^x
since f(0)=25
f(x)=25(0.40)^x

the number of bounces that it will take for rebound to be less than 1 will be:
25(0.4)^x<1
this can be written as:
0.4^x<0.04
introducing natural logs we get:
xln0.4<ln0.04
x(-1.39794)<(-0.39794)
x>(-0.39794)/(-1.39794)
x>3.513~4

[7.07] Choose the correct product of (6x + 2)2.


36x2 − 4


36x2 + 4


36x2 − 24x + 4


36x2 + 24x + 4

Answers

Answer:
36x^2 + 24x + 4

Explanation:
The perfect square has the following general formula:
(a + b)^2 = a^2 + 2ab + b^2

Now, we will expand the given perfect square based on the above general formula:
(6x + 2)^2 = (6x)^2 + 2(6x*2) + (2)^2
                 = 36x^2 + 24x + 4

Hope this helps :)

Corey spent 20% of his savings on a printer at Louie's ElectronisHow much did Corey have in his savings account before he bought the printer?

Answers

(printer cost) = 0.20 * (savings)
(printer cost)/0.20 = (savings)

savings = 5*(printer cost)

Whatever the cost of the printer was (information not supplied here), Corey's savings was 5 times that amount.

Answer:

5

Step-by-step explanation:

which of the binomials below is a factor of this trinomial

5x^2+14x-3

a. x-3
b. x+3
c. 5x+3
d. 5x-3

Answers

b: x+3 is your answer

Answer: Option 'B' is correct.

Step-by-step explanation:

Since we have given that

[tex]5x^2+14x-3[/tex]

As we know "Split the middle term":

[tex]5x^2+15x-x-3\\\\=5x(x+3)-1(x+3)\\\\=(5x-1)(x+3)[/tex]

Since it is quadratic equation so, it has 2 roots.

So, the roots are (x+3) and (5x-1).

Hence, Option 'B' is correct.

Elisa took out payday loan for $500 due in 2 weeks that charged an $80 fee. What is the periodic interest rate of the loan?

Answers

what are the options
c. 16% answer for Apex

PLEASE HELP!!!
The areas of a figure and its transformed image are the same. Which transformation could NOT have been applied to the original figure to create the image?     

A. Rotation of 90
B. Reflection across a horizontal line
C. Dilation by a scale factor of 0.5
D. Translation down 4 and then right 1

Answers

The answer to this question is the dilation with a scale factor of 0.5.  With a rotation, the size of the figure stays exactly the same - it is just turned.  With the reflection, the size also remains the same, it will just be flipped down or up (over/across the x-axis).  And, a translation does also NOT change the size of the figure.  It only moves the figure to a new position.  The dilation will create a similar figure (same shape, but NOT the same size).  In this case, the new figure will have side lengths half of the original figure.

The transformation that could NOT have been applied to the original figure to create an image with the same area is:

C. Dilation by a scale factor of 0.5.

To determine which transformation could NOT have been applied to the original figure to create the image with the same area, let's analyze each option:

A. Rotation of 90 degrees: When a figure is rotated by 90 degrees, the area remains the same.

This transformation is possible.

B. Reflection across a horizontal line: A reflection across a horizontal line (a horizontal flip) preserves the area of the figure.

This transformation is possible.

C. Dilation by a scale factor of 0.5: Dilation involves scaling a figure by a certain factor.

If a figure is dilated by a scale factor of 0.5, both its length and width are reduced to half, which means the area is reduced to one-fourth of the original area.

This transformation is not possible because it changes the area.

D. Translation down 4 and then right 1: A translation moves a figure without changing its size or shape. A translation down 4 and then right 1 would not change the area of the figure, as it simply shifts the figure's position.

This transformation is possible.

So, the transformation that could NOT have been applied to the original figure to create an image with the same area is:

C. Dilation by a scale factor of 0.5

Dilation by a scale factor of 0.5 would change the area, making it incompatible with the condition that the areas of the original figure and its image are the same.

For similar question on transformation.

https://brainly.com/question/5020733

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Consider the net of a triangular prism where each unit on the coordinate plane represents five feet. If a can of spray paint covers 25 square feet, how many cans of spray paint are needed to paint the outside of the prism blue?

Answers

Given:
Tetrahedron with vertices at
(0,0,0)
(5,0,0)
(0,5,0)
(0,0,5)

The surface area consists of 4 triangles, three of which each has an area
A1=bh/2=5*5/2=12.5

The slanted surface is an equilateral triangle of side
s=sqrt(5^2+5^2)=5sqrt(2).

The corresponding area is 
A2=(sqrt(3)/4)s^2=sqrt(3)/4*(5sqrt(2))^2=sqrt(3)/4*50
=12.5sqrt(3)

So the overall surface area of the tetrahedron is 
A=3A1+A2=3*12.5+12.5sqrt(3)
=12.5(3+sqrt(3))  ft ²
=59.15 ft ²  to two decimal places.

Number of cans =A/25=2.366 cans, so three cans are needed.

Jade is painting a rectangular wall. The wall is 4 1/4 yards long and 2 2/3 yards high. The formula for the area of a rectangle is A=bh. What is the area of the wall?

Answers

4 1/4 = 17/4
2 2/3 = 8/3

17/4 x 8/3 = 136/12 = 11 1/3 square yards

Answer:

11 1/3

Step-by-step explanation:

Please help me out asap!!! Thanks :)

Answers

the answer is -15.. if you look in the table it shows the answer and all you is plug in 5 for x and then you end up with -15

A point P (x, y) is shown on the unit circle U corresponding to a real number t. Find the values of the trigonometric functions at t.

Answers

sin(t)=8/17
cos(t)=-15/17
tan(t)=-8/15
sec(t)=-17/15
csc(t)=17/8
cot(t)=-15/8

Point P is on the unit circle U. The values of trigonometric functions at t are [tex]sin\theta=\dfrac{8}{17},\;cos\theta=-\dfrac{15}{17}[/tex][tex],tan\theta=-\dfrac{8}{15},\;cot \theta=-\dfrac{15}{8},\;cosec\theta=\dfrac{17}{8},\;sec\theta=-\dfrac{17}{15}[/tex].

Given:

From the given figure, the coordinate of point P is [tex](-\dfrac{15}{17}, \dfrac{8}{17})[/tex].

The point P is present on a unit circle U. So, in general, the coordinates of a point on the circle will be [tex](x,y)\equiv (cos\theta, sin\theta)[/tex].

By comparing the given coordinate with the general expression, the value sine and cosine function will be,

[tex]sin\theta=\dfrac{8}{17}\\cos\theta=-\dfrac{15}{17}[/tex]

Now, the other trigonometric functions will be,

[tex]tan\theta=\dfrac{sin\theta}{cos\theta}\\tan\theta=-\dfrac{8}{15}\\cot \theta=-\dfrac{15}{8}\\cosec\theta=1/sin\theta=\dfrac{17}{8}\\sec\theta=1/cos\theta=-\dfrac{17}{15}[/tex]

Therefore, the values of trigonometric functions at t are [tex]sin\theta=\dfrac{8}{17},\;cos\theta=-\dfrac{15}{17}[/tex][tex],tan\theta=-\dfrac{8}{15},\;cot \theta=-\dfrac{15}{8},\;cosec\theta=\dfrac{17}{8},\;sec\theta=-\dfrac{17}{15}[/tex].

For more details, refer to the link:

https://brainly.com/question/25090596

Draw the translation of LM along the vector (4, -5)

Answers

I think this is true:
[tex] \binom{0}{ - 2} [/tex]

the greatest common factor of −27x2yz5 + 15x3z3

Answers

we have that
−27x2yz5 + 15x3z3

we know that
27-------------> 3³
15-------------> 3*5
z^5-----------> z² * z³
x³------------> x² * x

substituting in the original expression

−27x2yz5 + 15x3z3---------->[-3³*x²*y*z³*z²]+[3*5*x²*x*z³]

[-3³*x²*y*z³*z²]+[3*5*x²*x*z³]-------> [3*x² *z³]*{[-3² *y*z²]+[5*x]}

the greatest common factor is [3*x² *z³]

Match each as a Compound (C) or Element (E)

Cu
HCI
CCI4
Co
HI
CH4

Answers

Cu is an element
HCI compound?
CCI4 compound
Co compound ?
HI compound
CH4 compound

What is the greatest common factor of 8xy^5−16x^2y^3+20x^4y^4 ?

A. 8xy^5

B. 2xy^3

C. 4xy^3

D. 4x^4y^5

Answers

The answer is C 4xy^3

Jesse took out a 30-year loan for $85,000 at 7.2% interest, compounded monthly. If his monthly payment on the loan is $576.97, how much of his first payment went toward note reduction(reducing principal)? Show your work.

Answers

the correct answer for this question is 66.97

Answer:

$66.97 is his first payment went toward reduction.

Step-by-step explanation:

Given : Jesse took out a 30-year loan for $85,000 at 7.2% interest, compounded monthly. If his monthly payment on the loan is $576.97.

To find : How much of his first payment went toward note reduction(reducing principal)?  

Solution :

First we find the interest of 1 month on a loan of $85,000 at 7.2% interest.

[tex]I=85000\times \frac{7.2}{12\times 100}[/tex]

[tex]I=85000\times 0.006[/tex]

[tex]I=510[/tex]

Interest of 1 month is $510.

Monthly payment = $576.97

Now, first payment or reducing principal is given by

F= monthly payment - interest of 1 month

F=$576.97- $510

F=$66.97

Therefore, $66.97 is his first payment went toward reduction.

A histogram is being made for the following list of data. 78, 92, 98, 87, 86, 72, 92, 81, 86, 92 If the length of each interval is going to be 6, how many bars will there be on the histogram? 4 5 6 7

Answers

The maximum value is 98, and the minimum value is 72
Therefore, the range is 98-72 = 26 
The bars, 26/6
               = 4.33
               ≈ 5 (to accommodate all the values)
Thus the number of bars will be 5.

solve each equation 2/3 (m - 6)=3

Answers

Hey there! :D

2/3(m-6)= 3

2/3m-4=3

2/3m= 7

m= 10.5

We can check it.

2/3(10.5-6)= 3

7-4=3

3=3

I hope this helps!
~kaikers
2/3(m-6)=3

multiply 2 by everything in fraction; keep same denominator for everything in parentheses
(2*m)/3 - (2*6)/3= 3
2m/3 - 12/3= 3

simplify 12/3= 4
2m/3 - 4= 3

Multiply everything by 3 to eliminate fraction
(3)(2m/3) - (3)(4)= (3)(3)
2m - 12= 9

add 12 to both sides
2m= 21

divide both sides by 2
m= 10.5

Check:
2/3(m-6)=3
2/3(10.5-6)= 3
2/3(4.5)= 3
(2*4.5)/3= 3
9/3= 3
3= 3

Hope this helps! :)

helppppppppppppppppppppppppppppppp

Answers

Answer:
10√3 which is the last option

Explanation:
√30 * √10 = (30*10)^1/2
                = 300^1/2

300 = 100 * 3
Therefore:
√300 = √100 * √3 = 10√3

Hope this helps :)

The graph of [tex]y= \sqrt[3]{x} [/tex] was shifted 5 units down and 4 units to the left. What is the equation of the resulting graph?

Please answer quickly!

Answers

Using translation concepts, it is found that the equation of the resulting graph is given by:

[tex]y = \sqrt[3]{x + 4} - 5[/tex]

What is a translation?

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, the changes are given as follows:

Shift down of 5 units, hence y -> y - 5.Shift left of 4 units, hence x -> x + 4.

Hence the equation of the resulting graph is given by:

[tex]y = \sqrt[3]{x + 4} - 5[/tex]

More can be learned about translation concepts at https://brainly.com/question/4521517

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Final answer:

The equation of the graph \\sqrt[3]{x} shifted down by 5 units and to the left by 4 units is \\sqrt[3]{x + 4} - 5.

Explanation:

The transformation of the graph of y = \\sqrt[3]{x} down by 5 units and to the left by 4 units is represented by the function y = \\sqrt[3]{x + 4} - 5. When a graph is shifted to the left by 'a' units, we replace 'x' in the equation with (x + a). Similarly, when a graph is shifted down by 'b' units, we subtract 'b' from the function, resulting in f(x) - b. Therefore, incorporating both transformations into the original function, we get y = \\sqrt[3]{x + 4} - 5.

Learn more about Graph Transformation here:

https://brainly.com/question/19040905

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If carpet cost$5 per square yard, what would it cost to carpet a room that is 5 yards wide and 22 yards long?

Answers

First you’d have to multiply 5 & 22, 5x22=110 and 110x5=550

So it’s 550

You buy a new laptop for
$299.99
$299.99
.
The sales tax is
6%
6%
.

What is the total cost for the laptop including the sales tax?


Answers

To find the total cost including the tax rate, we multiply by:
[tex]1 + \frac{tax}{100} [/tex]
So in this case we have to multiply by
[tex]1 + \frac{6}{100} = 1.06[/tex]
Therefore the price including tax is
[tex]299.99 \times 1.06 = 317.99[/tex]
Hence, $317.99
you would have to multiply it 299.99 ( .06) then youll get your answer . you have to change the percentage into a decimal. hope it helps 

The number of gallons of water,y, in a swimming pool is modeled by the equation y=7.5x+500,where x represents the time in minutes after the pump is turned on. How many gallons of water are in the pool if the pump is on for 200 minutes.

Answers

y = 7.5*200 +500
y = 1500 +500
y = 2000

2000 gallons are in the pool 200 minutes after the pump is turned on.

Lines p and q are perpendicular. If the slope of line p is 2, what is the slope of line q?

A. 1/2
B. -1/2
C. -2
D. 2

Answers

The meaning of perpendicular lines, are two straight lines that intercept each other. Their slopes are opposute reciprocal, meaning that it's multiplication is -1.

If the slope of line p is 2, then the slope of line q is -1/2.

The correct answer is letter B, -1/2.

Answer:

- 1/2

Step-by-step explanation:

I just did it

If the circle x2 - 4x + y2 + 2y = 4 is translated 3 units to the right and 1 unit down, what is the center of the circle?

Answers

Answer:

(5,-2).

Step-by-step explanation:

First, let's find the original center of the circle, we have

[tex]x^2 - 4x + y^2 + 2y = 4[/tex]

we are going to complete square adding and subtracting 4 for the x terms and 1 for the y terms

[tex]x^2 - 4x+4-4 + y^2 + 2y+1-1 = 4[/tex]

[tex](x-2)^2 - 4 + (y+1)^2 - 1 = 4[/tex]

[tex](x-2)^2+ (y+1)^2 - 5 = 4[/tex]

[tex](x-2)^2+ (y+1)^2 = 4+5[/tex]

[tex](x-2)^2+ (y+1)^2 = 9.[/tex]

The canonical formula of a circumference is [tex](x-h)^2+(y-k)^2=r^2[/tex]

Then, we have a circle with [tex]r^2 =9[/tex] and center (h,k)=(2,-1).

Now, if we translate the circle 3 units to right and 1 unit down, then all the points in the circle will be translated including the center. Especifically, the x values will be added 3 units and the y-vaues will be subtracted 1 unit, then the new center will be

(2+3,-1-1) = (5,-2).

I need help fast. Identify the apothem (a), the radius (r), and the perimeter (p) of the regular figure.

Answers

Final answer:

The apothem (a), radius (r), and perimeter (p) of a regular figure are defined as follows: the apothem is the perpendicular distance from the center of the figure to one of its sides, the radius is the distance from the center of the figure to any point on its circumference, and the perimeter is the total length of all its sides.

Explanation:

The apothem (a) of a regular figure is the perpendicular distance from the center of the figure to one of its sides.

The radius (r) of a regular figure is the distance from the center of the figure to any point on its circumference.

The perimeter (p) of a regular figure is the total length of all its sides.

PLEASE FULL ANSWERS! need all the help I can get

Answers

This critter is really a nasty piece of work. If you have a sister or daughter, I'd never let her date this question.

The question is What happens at 4 -- exactly.
The function at x =4 is determined by 2 * x or 2*4 = 8

But look what happens to the top and bottom functions when you get infinitely close to x = 4. You could let x = 3.99999 to see what happens to the top function

g(x) = x - 2 when x is less than 4. So ...
Put in g(3.99999) = x - 2
g(3.99999) = 3.99999 - 2 = 1.99999 which rounds to 2. That's nowheres near 8.

We have already shown that at this point this is going to be discontinuous. 2 does not equal 8. But just for fun, we should try the bottom function
Suppose x = 3.99999 again.
then g(3.99999) = sqrt(3.99999) which is almost 2. there's no way that will work.

Which answer describes the function f(x) = x^6−x^4 ?

neither

even

odd

Answers

to determine if it is even replace x with -x and see if the answer is identical.

 In this case, this function is even

Answer:

The function [tex]f(x)=x^6-x^4[/tex] is:

Even

Step-by-step explanation:

A function f(x) is even if:

f(-x)= f(x)

A function f(x) is odd if:

f(-x)= -f(x)

Here, we are given a function f(x) as:

[tex]f(x)=x^6-x^4[/tex]

[tex]f(-x)=(-x)^6-(-x)^4\\\\ =x^6-x^4\\\\=f(x)[/tex]

f(-x)=f(x)

Hence, the function [tex]f(x)=x^6-x^4[/tex] is:

Even

prove that root 7 is irrational by the method of contradiction

Answers

Let assume that [tex]\sqrt7[/tex] is a rational number. Therefore it can be expressed as a fraction [tex]\dfrac{a}{b}[/tex] where[tex]a,b\in\mathbb{Z}[/tex] and [tex]\text{gcd}(a,b)=1[/tex].

[tex]\sqrt7=\dfrac{a}{b}\\\\7=\dfrac{a^2}{b^2}\\\\a^2=7b^2[/tex]

This means that [tex]a^2[/tex] is divisible by 7, and therefore also [tex]a[/tex] is divisible by 7.

So, [tex]a=7k[/tex] where [tex]k\in\mathbb{Z}[/tex]

[tex](7k)^2=7b^2\\\\49k^2=7b^2\\\\7k^2=b^2[/tex]

Analogically to [tex]a^2=7b^2[/tex] ------- [tex]b^2[/tex] is divisible by 7 and therefore so is [tex]b[/tex].

But if both numbers [tex]a[/tex] and [tex]b[/tex] are divisible by 7, then [tex]\text{gcd}(a,b)=7[/tex] which contradicts our earlier assumption that [tex]\text{gcd}(a,b)=1[/tex].

Therefore [tex]\sqrt7[/tex] is an irrational number.

Final answer:

To prove that √7 is irrational, we assume the opposite and show that it leads to a contradiction. We start by assuming that √7 is rational and can be expressed as a fraction. By squaring both sides of the equation and simplifying, we get an equation that leads to p and q being divisible by 7, which contradicts our initial assumption. Therefore, √7 must be irrational.

Explanation:

To prove that √7 is irrational using the method of contradiction, we assume the opposite, which is that √7 is rational. This means that it can be expressed as a fraction p/q, where p and q are integers with no common factors other than 1. We can then square both sides of the equation (√7)² = (p/q)² and simplify to get the equation 7 = p²/q². Rearranging, we have p²= 7q².

From this equation, we can deduce that p² is divisible by 7, which means p must also be divisible by 7. Let's represent p as 7r, where r is another integer. Substituting back into the equation, we get (7r)² = 7q², which simplifies to 49r² = 7q². Dividing both sides by 7, we have 7r² = q². This implies that q² is also divisible by 7, so q must also be divisible by 7.

However, if both p and q are divisible by 7, this contradicts our initial assumption that p/q has no common factors other than 1. Therefore, our assumption that √7 is rational must be false, and hence √7 is irrational.

In the diagram below, m = 96 and m = 114. What is the measure of
JPM?

Answers

When there are two chords intersecting inside of a circle, there are four angles that are formed from this intersection. At the intersection, there are two sets of congruent vertical angles formed. 

Angle Formed by Two Chords = 1/2(Sum of the Intercepted Arcs)

m<JPM = 1/2 (114 + 96)  = 1/2 (210) = 105

Answer:

A ) 105

Answer:

C.Apex(105)

Step-by-step explanation:

Other Questions
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